There's an easy answer to this question: Tamina is a widowed émigré from Communist Czechoslovakia who works a dead-end job in a little café in some boring Western European town.
But Kundera values her much more highly than that. Tamina is his novel: "It is a novel about Tamina, and whenever Tamina goes offstage, it is a novel for Tamina. She is its principal character and its principal audience, and the other stories are variations on her own story and meet with her life as in a mirror" (VI.8.2).
Kundera wants to explore the phenomenon of forgetting, of losing memories that are both crucial and dear to individuals and to countries. Tamina is the poster child for forgetting: she spirals into existential despair because she's losing contact with the mental image of her dead husband through the natural processes of time.
While forgetting is something that just happens, Tamina can't find any context for her life outside of the relationship she had with her husband, Pavel. She can't move forward without him because he is her framework. With the disappearance of her memories of Pavel, Tamina finds that her own identity begins to crumble:
For Tamina is adrift on a raft and looking back, looking only back. Her entire being contains only what she sees there, far behind her. Just as her past contracts, disintegrates, dissolves, so Tamina is shrinking and losing her contours. (IV.5.9)
There is no point for Tamina to dwell in the present and interact with the people around her because these people have no understanding of who she is or where she came from. That whole part of her life in Prague is just...gone.
Without the presence of her husband—even if it's only in her mind—Tamina's isolation is complete: "I imagine the world rising higher and higher around Tamina like a circular wall, and that she is a bit of lawn down at the bottom. Growing on that bit of lawn, there is only a single rose, the memory of her husband" (IV.4.4).
Kundera creates Tamina as a counterbalance to his emphasis on the importance of memory. For some, memory isn't a good thing. It undermines the work of everyday life, of moving forward. Tamina's journey in this novel is not meant to be a cathartic one; she's not headed for redemption or healing.
Because Tamina is desperately grabbing for memories of her past life with Pavel, she decides that she must retrieve the personal notebooks she left behind in Prague. They are a record of her married life, and she's convinced that this will be her salvation: if she can prop up her failing memory, she won't have to face the bleakness of the present.
But Tamina comes to understand that access to her thoughts is not enough. She wants those notebooks intact, untouched by other hands or eyes. It kills her to think that someone might have read through her private thoughts in the years that she's been separated from them:
She realized that what gave her written memories their meaning and worth was that they were intended for her alone. As soon as they lost that quality, the intimate tie binding her to them would be cut, and she would be able to read them no longer with her own eyes but only with the eyes of readers perusing a document about some other person. Then even she who had written them would become for her some other person, an outsider. (IV.15.3)
This extra requirement makes the task impossible; once Tamina adds it, the whole project is doomed. She can never really know if anyone has bothered to read the books and whether or not they valued the contents. Tamina's heartbreak over the possible violation of her notebooks seems to make the ickiness of her sexual encounter with Hugo even worse.
After her disappointment over the notebooks, Tamina falls further into isolation. It's not till the mysterious Raphael has her at the edge of the muddy cliff that everything comes together for her: "Whoever wishes to remember must not stay in one place, waiting for the memories to come of their own accord! Memories are scattered all over the immense world, and it takes voyaging to find them and make them leave their refuge!" (VI.8.9).
It's a great flash of understanding—and just the thing Tamina needs to get on with her life. But it's too late—she's already on her journey to the island of childhood. She's getting the thing she wished for most: a life without the weight of the past.
Tamina should have been more careful with what she wished for: a life without weight, as Kundera says, can be a blessing or a curse. Erasing the past can mean a carefree existence, as Tamina finds out: "She had fallen far back to a time when her husband did not exist, when he was neither in memory nor in desire, and thus when there was neither weight nor remorse" (VI.15.1).
But it also means a life without context, purpose, or progress. Tamina plays inane games and endures the creepy caresses of the children. She feels pleasure, but it's without the consent of her soul. And in the end, Tamina is not a child. She realizes—too late—that she can't literally live in the past. The violence of the children against her is not because they are evil, says Kundera. It's because she is "other": "Her misfortune is not that the children are bad but that she is beyond their world's border" (VI.23.3).
Tamina's story sends a powerful message about the proper use of memory and the past: it's not a place to live, but we really can't live without it. To deny the past is to negate our own being, to revise our identities in unnatural ways. Those who try to do it will suffer unspeakable sorrow.